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Stefan–Boltzmann equation for the power radiated from a black body in terms of its temperature.
Thornton
Global radiation depending on latitude
Sun declination
Eccentricity factor for calculation of extraterrestrial radiation (Fortin et al., 2008)
Daily extraterrestrial radiation as developed by Sellers 1961 (cit. in Fortin et al. 2008, and Cai et al. 2007) note: formula of sun declination wrong in Fortin et al. 2008
Ratio between diffuse and total solar irradiance after Friend et al., 2001
Lizaso et al. 2005
Daylength
Daylength period
Saturated vapor pressure according to hamon:1963a
When foliage temperature is above 0oC, saturated vapor pressure is calculated as:
\[ svp = 0.61078 * \exp(17.26939 * \frac{T}{T + 237.3}) \]
When foliage temperature is below 0oC, it is:
\[ svp = 0.61078 * \exp(21.87456 * \frac{T}{T + 265.5}) \]
Annual mean temperature
Incoming longwave radiation is given by:
\[ LWR_{in} = \varepsilon \sigma T^4 \; , \]
wherein \( \varepsilon, \sigma, T \) refer to the emissivity, the Stefan-Boltzmann constant and air temperature, respectively.
The emissivity \( \varepsilon \) has two components , i.e., emissivity under clear ( \( \varepsilon_{cl} \)) and clouded sky ( \( \varepsilon_{cl} \)):
\[ \varepsilon = (1 - f_{cl}) \varepsilon_{cs} + f_{cl} \varepsilon_{cl} \]
The partitioning coefficient \( f_{cl} \) refers to the cloud fracion. For \( \varepsilon_{cl} \), a constant value of 0.976 is used [greuell:1997a].
Clear sky atmospheric emissivity
Emissivity of incoming longwave radiation under clear sky conditions is calculated based on vapour pressure \( vp \) [brunt:1932a] :
\[ \varepsilon_{cs} = B_c + B_d \sqrt{vp} \]
The parameters \( B_c \) and \( B_d \) are set to 0.53 and 0.212, respectively [kraalingen:1997a].
Cloudiness
Cloudiness is derived from global radiation using the Angstrom formular:
\[ f_{cl} = \frac{\frac{SWR}{SWR^{\ast}} - A}{B} \]
using the Angstrom parameters \( A = 0.29 \) and \( B = 0.52 \) [kraalingen:1997a].
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